Affine
transformations: A linear transformation that
might not preserve angles.

IFS are a set of affine
transformations (or "rules"), that map points in the plane by
randomly chosing which of the rules to apply at each stage of the iteration
according to some predefined probability.

Also, to get the angle from the coefficients: ANG = arctan (C/A) = arctan
(-B/D)

EXAMPLES:

1) To generate the Koch Curve:

GENERATOR

Piece 1: 1/3 REDUCTION

Piece 2: 1/3 REDUCTION, 60 deg ROTATION, followed by a 1/3 TRANSLATION
in the X direction.

Piece 3: 1/3 REDUCTION, -60 deg ROTATION, followed by a 1/2 TRANSLATION
in the X direction plus a 0.287 TRANSLATION in the Y direction.

Piece 4: 1/3 REDUCTION, followed by a 2/3 TRANSLATION in the X direction.

Note that PROB (or "W" for Weigth) is calculated by the IFS
program from the coefficients A, B, C, and D, by calculating DET (Rule i)=
ABS(A*D-B*C) for each rule and normalizing PROB (Rule i) = DET (Rule i)/(SUM
ALL DETs)